First of all, I doubt that there's a direct canonical explanation for this, as probably it's just a film matter.
However... we can guess that, although actually by the time of SW:ANH almost every stormtrooper isn't a clone, probably it's instruction is the same from the early Empire days, when the clones where left handed (I didn't know that) and trained to fight and shoot from a "left guard".
The use and design of firearms has a heavy component on the user handling: the placement of adjustment buttons, safes, exit scapes, etc... are different on a weapon designed for left-handed use than on a weapon designed for right-handed use.
We can assume that, if the whole original stormtrooper contingent was left handed, their weapons would be designed for their use with a "left guard"; so as more volunteers enlist and less clones are needed more right handed soldiers start to receive stormtrooper training and equipment, it's designed for left handed people and taught from left handed instructors.
On the long term we can assume that an army that builds originally from only left handed people will train all it's soldiers that way just for procedural efficiency.